Exponential stability of Euler integral in the three--body problem
Mathematical Physics
2018-08-24 v1 Dynamical Systems
math.MP
Abstract
The first integral characteristic of the two--centres problem is proven to be an approximate integral (in the sense of N.N.Nekhorossev) to the three--body problem, at least if the masses are very different and the particles are constrained on the same plane. The proof uses a new normal form result, carefully designed around the degeneracies of the problem, and a new study of the phase portrait of the unperturbed problem. Applications to the prediction of collisions between the two minor bodies are shown.
Cite
@article{arxiv.1808.07633,
title = {Exponential stability of Euler integral in the three--body problem},
author = {Gabriella Pinzari},
journal= {arXiv preprint arXiv:1808.07633},
year = {2018}
}
Comments
74 pages, 6 figures. This research is funded by the ERC project 677793 Stable and Chaotic Motions in the Planetary Problem